# 11.2 Operations on Functions

In Chapter 5, you solved systems of linear equations through substitution, addition, subtraction, multiplication, and division. A similar process is employed in this topic, where you will add, subtract, multiply, divide, or substitute functions. The notation used for this looks like the following:

Given two functions and :

When encountering questions about operations on functions, you will generally be asked to do two things: combine the equations in some described fashion and to substitute some value to replace the variable in the original equation. These are illustrated in the following examples.

Example 11.2.1

Perform the following operations on and .

1. Addition yields , which simplifies to .
2. Subtraction yields , which simplifies to .
3. Multiplication yields , which simplifies to .
4. Division yields , which cannot be reduced any further.

Often, you are asked to evaluate operations on functions where you must substitute some given value into the combined functions. Consider the following.

Example 11.2.2

Perform the following operations on and and evaluate for the given values.

Composite functions are functions that involve substitution of functions, such as is substituted for the -value in the function or the reverse. Which goes where is outlined by the way the equation is written:

The more conventional way to write these composite functions is:

Consider the following examples of composite functions.

Example 11.2.3

Given the functions and , evaluate for:

# Questions

Perform the indicated operations.

1. Find

2. Find

3. Find

4. Find

5. Find

6. Find

7. Find

8. Find

9. Find

10. Find

11. Find

12. Find

13. Find

14. Find

15. Find

16. Find

17. Find

18. Find

19. Find

20. Find

Solve the following composite functions.

1. Find

2. Find

3. Find

4. Find

5. Find

6. Find

7. Find

8. Find

9. Find

10. Find

Answer Key 11.2

## License

Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.